On Tuesday, senators will debate a more modest expansion of the background checks that has won bipartisan support and bolstered gun control supporters' hopes of pushing something through Congress.

The checks are now required only for sales through licensed gun dealers, while the amendment would subject all sales at gun shows and advertised forums like the Internet to the requirement, exempting noncommercial transactions such as those between relatives.

In a win for gun-rights advocates, the amendment also would make it easier to transport firearms across state lines and gradually shorten the maximum waiting time - from three days to one - for people whose gun applications are being processed by the background check system.

"All law-abiding gun owners in America should love this piece of legislation," Sen. Joe Manchin, D-W.Va., said in an interview.

As debate proceeds, some potential amendments could broaden gun rights and weaken supporters' backing for the overall bill.

One proposal is by Sens. Lindsey Graham, R-S.C., and Mark Begich, D-Alaska, who say it would improve how the background check system keeps weapons from people with certain mental problems, though critics say it would make it harder in some cases to do so. Another possible amendment would require states to recognize permits for carrying concealed weapons issued by other states.

In Thursday's vote, 50 Democrats and two Democratic-leaning independents were joined by 16 Republicans in voting to begin debate on the overall legislation.

Twenty-nine Republicans and two Democrats facing re-election next year in GOP-leaning states voted "no" - Alaska's Begich and Mark Pryor of Arkansas.